At baccarat the definition of asymmetry and symmetry is particularly intricated for several reasons:

- the model is slight asymmetrical at the start (B>P)

- the model is affected by a huge first-step asymmetrical distribution of cards, specifically of key cards

- the model is affected by a huge second-step asymmetrical distribution of third(s) card(s)

- the model is finite and dependent, meaning that each situation (hand dealt) won't cross through the exact same parameters.

Overall and simplifying the issue, we might infer that symmetrical events are just "incidents" made along the way.
After all statistics give us plenty of examples where asymmetry will lead over the symmetry, the latter now intended as a steady expected probability happening for long.

Actually at baccarat there's no symmetry involved other than by coincidental factors and when some low levels of asymmetry are surpassed, more often than not a slight subtle force will shift the results in order to deny a kind of "balanced" results.

Therefore the rule to follow is expecting "low levels of asymmetry": whenever this rule seems to be "violated" best action to make is staying still (no betting) or to wager that the lowest levels of asymmetry will remain as silent.

After all we have strong reasons to think that cards are randomly arranged to get more asymmetrical patterns than symmetrical patterns and when this isn't true is just for a temporary and coincidental short term effect.

Examples of typical asym or sym patterns

ABAA = asym
ABA  = sym

AABBB = asym
AABBA = sym

AAABA or AAABBA = asym
AAABBB = sym

Overall we could accept the idea that asym=sym, yet we should be more interested about how many sym events will shift into asym events or vice versa and, more importantly, at which level of asymmetry or symmetry. Per every shoe played.

Now we might use a formula based upon that asym-asym > asym-sym; sym-asym > sym-sym for the most probable asymmetry/symmetry levels of apparition (0, 1 and 2).

We know that an asym/sym/asym sequence lasting for long is the least occurence to happen and the same is about long sym/sym successions.
The remaining probability world is what we should be interested to focus about as proportionally taken (remember the 0.75 probability to happen) asym/asym..., sym/asym and sym-sym/asym patterns are way more probable to naturally come out so maybe enticing (I've sayed "maybe" as a simple flat betting scheme will get the best of it) a multilayered progressive scheme actioned by one or more two losing sym sequences happening at different sections of the shoe.

Assigning a 0.75 general winning probability to a asym/sym independent model, the average expected W/L ratio is 3:1, so unbeatable for the vig or P asymmetrical probability.
In reality baccarat slightly endorses the asym patterns formation in the way that each asymmetry level will be more probable than the symmetry counterpart.
Naturally the sure asymmetry will make coincidental symmetrical patterns along the way, that's why  we have to restrict their appearance by assigning or not them to a more likely sequences category.

I know, that's all rattlesnake.sh.it.
Fortunately. 

as.

IMO at baccarat the only reason why we could win is because of the more likely card distribution ranges.
The actual results do not necessarily be the by product of more likely card distribution ranges as (beyond the natural variance) there still exists the important factor regarding the shuffling more or less randomness.

Our data had taught us that a perfect randomness or a slight defect of randomness will go to our favor as best represents the "more likely card distribution" ranges.

Bad shuffled shoes need too much complicated algorithms to be resolved (approximated) and of course we never know how "bad" a shoe is shuffled and more importantly the more probable patterns to look for.

In poor words, we'll win a lot or lose a lot when shoes are badly shuffled with 0 impact of skills, whereas perfect random or near perfect random shoes will give us plenty of informations to draw on.

more later

as.   

A personal test for bac randomness

Our group is made by frequentist probability lovers, in the sense that we like to collect data coming out from the same exact source and then building a probability theory.

Even the "same source" concept could be a volatile definition: think about shuffling machines operating at two alternate shoes lasting for a X time (number of shuffles per each shoe).
We've found important differences if the same shoe did undergo one or two shuffles or multiple shuffles.

Therefore if we want to exploit the "average" card distribution tool, we want to play at properly shuffled shoes.
Remember the comparison with black jack: low cards-neutral cards-high cards decks (in any LNH sequence) completely deny a card counter math advantage.
Of course such situation could easily happen for natural reasons, but we never know if it seem to appear for "too much" long.

At baccarat we've personally devised two valuable main tools to take care of in order to approximate whether a shoe is really randomly shuffled or not.

a) the math advantaged two-initial cards points losing "too many times" despite of their math propensity to win;

b) a higher than average ratio of hands resolved by 6 cards.

Of course those are the two main factors, there are other minor parameters to look for.

Realize that there's no way to win at baccarat itlr if our bets will get the inferior 2-card initial point as the number of drawouts will be underdog to get a long term edge.
Thus whenever the drawouts are coming out "too often", we theorized that that shoe was improperly shuffled. So unplayable.

Hands resolved by 6 cards is an additional factor to look for and is related to the high neutral card density (more than 30%) along with the 6s,7s,8s and 9s class (again more than 30%), then to  other less likely card combinations forming natural points as 5-4, 5-3, 4-4 or standing points as 5-A, 5-2, 4-3, 4-2 or 3-3.

Card distributions not forming those situations AT BOTH SIDES for long are relatively rare and when they're not (that is they are coming out too often) we could assume a kind of randomness bias.

Paradoxically it's better to move around a strong good or strong bad choice than navigating into a more undefined world where too many cards will dictate the actual result.
That's because an overalternating shifted world will be the least situation to happen.

as. 

Believe me, you can't be wrong by properly exploting the asymmetry.

Say we want to adopt a multilayered progressive scheme.

We have three different fictional players betting for us.

#1 will constantly betting toward clustered asym spots up to a loss, then he'll wait for a new asym situation to restart the betting.

#2 will wait for a symmetrical spot to show up (sometimes it'll take quite a long time and that should give you the idea of what I'm talking about) then wagering toward one asym spot then stops its action letting #1 to restart the betting.
If he loses, #3 come in play.

#3 will wait for TWO asym spots to show up then wagering toward one asym spot then stops its action letting #1 to restart the betting.
If he loses, the action is stopped for every player (#1, #2 and #3) until a fresh asym spot shows up.
And so on.

After each player had lost three times in a row, we'll raise the bet for that specific player by a 10% or 20% amount knowing that the only harsh "enemy" spots making ALL three players to lose in a row are those forming one asym isolated spot followed by three (or more) symmetrical spots.

When such unlikely thing happens (all players losing) we have reasons to even double our standard bet then staying at this betting level until a full recover happened.

In fact asym-sym-sym-sym-...-asym situations coming out in a row are just an exception.

See you next week

as.

"I'll take not just one step, but two steps forward with the knowledge you've shared. However, your theory is quite challenging. I think it'll take some time to fully grasp and apply it to my betting strategy, probably because your level is very advanced. Even so, I truly appreciate the insights you've provided. I'll take some time to make them my own, and once I do, I'll follow up with any questions I have."

This version keeps the meaning intact while making it flow smoothly in American English. Let me know if you'd like any further tweaks! 😊

You're fine LP and thanks for your interest.

This thread is made upon ideas, findings and a very deep interest about this complicated game where we didn't take anything as granted.
Therefore our strategies are mainly based upon statistical findings applied to volatile productions very often improperly labeled as "randomly distributed".

Whether is impossible to read randomness (providing each trial to be as perfectly independent from the previous one), we know that distributions sooner or later will take more likely distributions in relationship of the actual shuffling factor.

The problem of moderate/strong unrandomly shuffled shoes is that it's more difficult to spot an "average" key card distribution along with math advantaged hand ranges, in a sense high/low cards are more clumped than expected by running a true random model.

Of course if a given strategy works at perfect random or close to perfect random shoes, anything different than that (unrandom world prevails) might be attacked by a kind of opposite method. So maybe privileging more the SYMMETRICAL less likely feature.
But doing this we could find ourselves in the unwanted world of full uncertainty unless a same shoe is shuffled several times by the same biased procedure.

So players thinking that every shoe dealt in different circumstances will be distributed by the same random features actually commit a big mistake erasing a possible edge.

more later

as.

At baccarat itlr the asymmetrical propensity will be slight superior than the symmetrical one, yet many shoes could produce long situations of sym patterns posing a real threat to any not carefully conceived plan. Remember that the HE is always burdening us.

So less is more, by any means. Meaning that lower is the amount of our bets better will be our "precision" of being more right than wrong. At the cost of missing some profitable situations that anyway itlr will save us a lot of money.

Suppose the core (discarding some initial and final hands) of the shoe A/B patterns went as: (AS=asymmetrical pattern= +1 and S=symmetrical pattern= -3), Big Road considered.

AS-AS-AS-AS-AS-AS-S-AS-AS-S-AS-AS-S-S-AS-S-S-S-AS

At the end this is a strong Symmetrical shoe as AS=12 (=+12) and S=7 (=-21). Total -9.
Yet AS clusters (3) are equal to AS isolated events (1); S patterns came out as isolated two times and double clustered one time (S-S) and only one time clustered more than two times in a row (S-S-S).

Another shoe:

AS-AS-S-AS-AS-AS-S-AS-AS-AS-AS-AS-AS-AS

AS= 12 (+12), S= 2 (-6).

Here this shoe haven't balanced the previous one (-9), now (+6) but at this shoe there are no "unexpected" distributions capable to be harmful to our plan.
AS= always clustered and S= always isolated.

Another shoe:

AS-AS-AS-S-AS-AS-AS-AS-AS-AS-AS-AS-AS-S-AS-S-(-1)

AS=13, S=3 plus -1 that is a total of +3.

Moreveor even here AS clusters are 3 and AS isolated events (at the end of the shoe) are just 1.

Let's see what happens by respectively running our random walk getting a different pace than the Big road succession.

shoe #1: AS-AS-S-AS-AS-AS-AS-AS-AS-AS-AS-AS-AS-AS-S (AS=13, S=2) that is +13 and -6

shoe #2: AS-S-AS-AS-S-S-AS-AS-AS-AS-AS-S-AS (AS=9, S=4) that is +9 and -12

shoe #3: AS-AS-AS-AS-S-AS-S-AS-AS-AS-AS-AS-(-1) (AS=10, S=2 plus -1) that is +10 and -7

Even though after having collected thousands and thousands of real live shoes data we've managed to set up the best performing random walk catching the most likely average card distribution, we'll see that, generally speaking, the least patterns to look for are those forming symmetrical patterns for long. Providing to assign the "asymmetrical/symmetrical" feature up to a point.

So to simplify the issue, symmetrical spots are:

1) ABAB or BABA

2) AABBA or BBAAB

3) AAA(...)-BBB(...) or BBB(...)-AAA(...)

Then, asymmetrical spots are:

1) ABB or BAA

2) ABAA or BABB

3) AABA or BBAB

4) AAA(...)BA or BBB(...)AB

5) AAA(...)BBA or BBB(...)AAB

Obviously a deep selected betting plan must take into account how many times any first or second level of asymmetry came out in a row or not, a thing we'll take care very soon.

as.

Hi Asym

"...So less is more, by any means. Meaning that lower is the amount of our bets better will be our "precision" of being more right than wrong. At the cost of missing some profitable situations that anyway itlr will save us a lot of money...."

     I concur. This is one of most important attributes a successful player can posses(i.e., selecting or shopping for the best value bet).
I observe many players approaching the game like someone entering a shopping mall on payday. They buy a lot of merchandise(bets) that are not priced at a good value.

One should look at baccarat wagers just like shopping. Sometimes the wager is worth more than what we pay for it and sometimes wagers are selling for a price greater than their value. Optimally we should shop to pay $48 for a $52 dollar wager. Sometimes there are even better deals. However, often there may only be a half dozen or so good deals per shoe.

Cheers,

Hi AsymBacGuy/hope you had a good week at the tables.

re:Your post awhile back about your approx edge of 3.46% net as shown in the excerpt below. I meant to ask you a question back when u posted but it was late at night /I guess I forgot about it.

Q: Is this 3.46% correlated to the ACV of 3.46 or just coincidental???
Thx in advance.
-------------------------------------------

From post #1233

"..Our estimated edge

Since we cannot use our algorithms in real play and not trusting (mainly for technical reasons) online games, we're forced to approximate at best an already approximating way of considering an average card distribution. Nonetheless at the end our average edge lines up at around 3.46% after vig.
It's a real big advantage but unfortunately performing huge fluctuations related to the actual shoe card distribution..."

edit

ACV= Average Card Value


thx,kfb

Hi KFB!

Ouch, I guess it's just coincidental...a weird coincidence though.

Never investigated the ACV but I know you don't miss anything...


One should look at baccarat wagers just like shopping. Sometimes the wager is worth more than what we pay for it and sometimes wagers are selling for a price greater than their value. Optimally we should shop to pay $48 for a $52 dollar wager. Sometimes there are even better deals. However, often there may only be a half dozen or so good deals per shoe.

Can't agree more on that.

as.

But what are the more likely AS/S occurrences along any shoe dealt?

And are there ploys to avoid strong negative deviations?

See you later

as.
   

The main problem about A/S (A= asymmetrical patterns, S= symmetrical patterns) occurences is that several times just one hand that went "wrong" will transform sure AS more likely sequences into a "long" S one, so disrupting a more probable flow.

Consider this A/S sequence.

A-S-S-S-S-A-A-A-A-S-A-A-A

In this bac succession the S marked in bold/red was a more natural opposite winning side (actually was a standing 7 point vs a 4 point that catched a third card 4) so more likely to produce a AS hand than a S hand; thus the above sequence would be read as:

A-S-S-A-S-A-A-A-A-S-A-A-A

And actually this is, by far, the most likely A/S situation happening, that is a fair number of A clusters and a "limited" number of singled or doubled S events.
 
Obviously such "unsound math" hands could easily go at our favor (that is forming A events where S situations were more supposed to show up) but we shouldn't be so happy to win such hands for long.

So solely playing for A events is the best action to make, yet possible consecutive shoes not fitting our plan will pose a real threat to our plan in terms of variance.

In order to set up a multilayered betting scheme (or a super selected flat betting method) we must take into account the WORST possible scenarios, that is a strong very very unlikely distribution of shoes not fitting the "average shoe" requisites.

I talked about shoes and not about hands.

Here's a brief list of real played shoes at HS rooms (preordered shuffled shoes), presented in the natural succession we've encountered them. Our random walk was utilized but event the big road succession will fit the concept. 
Feel free to re-arrange such shoes in the worst possible sequence.

For the purpose of the S average distribution I'll mention only S sequences (0.25% general probability to appear).
1= one S event
2= two consecutive S events
and so on

1-1-1-3

1

1-1-2-1

2-1

2-1

2-1

1-2

2-1

1-1

1-1-1-1

2-1

1-2

1-2

1-1-1

1-4

2-1-2-1

1

0

2-1-1-1

1-1-1

1-1-1-2

1-1-1-1-(2)

1-(2)

1-1-1-1

1-1-2

2-2-1

1-2

1-1-1

1-1-1-1-(2)

1-1

1-2

2-1-1-1-1

1

1-1

1-2-1

2-2

4-1

1-1-1-1-(2)

1-1

1-1-1

1-2

1-1

1-1-2-1

1-2-1-1-2

2

1-2

1-1-1

1

2-1-1

3-1-2

1-1-1

1-2-1-1

2-1

1-1-1-1-2

1-1-2

1

1-1

1-1-1-(2)

2-1-(2)

1-1-(2)

1-1

1-1-2

2-1-1-1

3-2-1

3

1-1-1

1-2-1

2-1-2

1-1-1

1-1-1-2

2-1-2-1

1-1

1-1

1-1(2)

1-1-1

1-1-3-1

1-3-1-1

1

1-1-1-1

1

1-1

1

1-1

1-1-1-1

1-2-2-(2)

2

1-1

1-3

1

1-1-1

1-2-1

1-1-1-1-(2)

1

1-2-1-1

1-1

1-2-1

1-1

1-1-2

1-1-1-1

1-1

1-1-2

1-2

1-1-3

2-1-2

1-1

1

1-1-2

1-2-1-1-1

1-1-1

2-1

1-2

1-1-1-1

1-1-2-1

2

1-1-1-1

1-1-1

2-1-1-1

1-2-1

1-1-3

1-1-(2)

1

1-1-2

1-1-2

1-1

1-1-1-1

3-3

1-1

1-2

2-2

2

1-4

2

1-1-2

2

1

1-1

1-2-1-1-1

2-1

2

1-1-1-2

1-1-1-(2)

1-1

1-2-1

1-1-1

1

4-3

1-2-1-1-1-1

2-1-2-1

1-1

1-1-(2)

1-1

1-1-1

1-1

2-1

3-2-1

2-2

2-1-1-1-1

1-1-1

1-3

1-1-1-1

1-1-1-(2)

1-1-1-2-1

oOoOo

Well, are those sequences performing a kind of "more likely patterns" in terms of numbers?

Notice that whereas the definition of A pattern is quite easy, the definition of a S pattern stops after the first level of symmetry happening.

So a (AABB)AB pattern (S pattern) should be considered as equal to a (AABBAABBAABB...) pattern, the same about consecutive patterns as AAABBBB or AAAAAAAABBBBAAABBBBBB, etc.

Sayed in another form, S patterns are those back to back patterns formed by the same or superior quantity related to the previous pattern up to the old 3-step degree.

Notice that more S numbers are displayed and shorter were the A sequences and vice versa.

Thus instead of guessing the unguessable, try to assign a deviation value to each fictional player  wagering for us and betting towards more probable specific levels of less likely symmetry.

P1 will bet towards level 1 of symmetry, so waiting the appearance of 1-step events of symmetry then wagering for the symmetry to stop after a given negative deviation happened.

P2 will bet towards level 2 of symmetry, so waiting the appearance of 2-step events of symmetry then wagering for the symmetry to stop after a negative deviation happened.

Px is our "id.iot gambler" so endlessly wagering towards the asymmetry, always considered by clusters. So meaning that it doesn't start the action until an asymmetrical event had shown up.

Merging the three players action together the W/L ratio at carefully selected spots will be way higher than 0.75.
So capable to erase and invert the HE.

as.

Example.

We know that per every shoe dealt the probability to get all or just one asymmetrical patterns is very low.
Therefore more than one symmetrical pattern MUST come out at some portion of the shoe.

Since we are not belonging to the category of those id.iots thinking that it's possible to read randomness or profitably following patterns, we must be prepared to face symmetrical patterns that we empirically labeled as "unprofitable".

Now it's up to us whether we want to select at most our betting opportunities or to hope we'll able to humanly guess a greater than 50% of total situations.
The latter scenario is what really fuels the game and casinos' profits.

Gambling experts of my a$$ teach us that every hand is a new hand no matter what.

Bighornsh.it.

Since cards are surely asymmetrically distributed, related results will be surely asymmetrically distributed.
Maybe sometimes results will take a kind of symmetrical shape for quite long but that's not the rule.

So let's falsify such hypothesis and starting to bet towards symmetry.
You'll go broke very soon or at least sooner than by wagering a kind of asymmetrical approach.

As long as symmetrical patterns will be consecutively placed by lower proportionally levels than asymmetrical patterns we will be in good shape.

We'll be back on this issue in a couple of days.

as.